Dicke models

Study of Antigravity in an Model and in Brans

Emergent crystallinity and frustration with Bose-Einstein condensates in multimode cavities. A compact flat geometry can be adopted, as seen in. Ion traps combined with high-Q cavities may offer new ways to realize the Dicke model and observe all the phase transitions and demonstrate entanglement. The system that we consider is composed of N biased qubits coupled to a single-mode bosonic field. The superradiant phase transition was originally predicted by the model of , which assumes that atoms have only two energetic levels and that these interact with only one mode of the electromagnetic field. And, finally, a brief conclusion is presented in §6. As a result of having a cavity that is not completely enclosed, spontaneous emission from individual ions is possible.

Study of Antigravity in an Model and in Brans

Collective cooling and self-organization of atoms in a cavity. However, as the technology for making high-Q optical cavities improved, it became possible to reach a strong-coupling regime in the optical domain with high-quality, small-volume, optical cavities. Universal digital quantum simulation with trapped ions. Self-organization of a Bose-Einstein condensate in an optical cavity. Above the critical coupling value, the Eq.

Study of Antigravity in an Model and in Brans

Observation of the Bloch-Siegert shift in a qubit-oscillator system in the ultrastrong coupling regime. However, the different atomic transitions are replaced by transitions between momentum states. Quantum chaos triggered by precursors of a quantum phase transition: The Dicke model. Because ion traps can maintain the position of ions in a cavity, the possibility exists for realizing the Dicke model with a fixed number of ions. These quantum simulations will contribute to the observation of quantum dynamics not accessible in current experiments.

Gauge invariant formulations of Dicke

The frequency scheme of the protocol is shown in. Discussion In order to capture the physical realization of the simulation, we plot in the behavior of the transmon-resonator system during the simulation protocol. When , the left hand side of Eq. These decay processes break the cooperativity of the system, while the cavity loss Γ does not. All these qualities make them ideal candidates for demonstrating collective and single-atom cavity-field quantum effects as oscillations of energy between the atom and cavity field can take place before decay becomes significant. The energy levels are shown for different numbers N of atoms and excitations n. The spin-0 case has been omitted from the figure.

Study of Antigravity in an Model and in Brans

The decay rate γ 0 is not the same quantity as the sideways emission at the rate γ, as shown in. This is confirmed by performing a spectroscopy of the eigenvalue spectrum by adjusting the detuning of the qubits from the resonator frequency and mapping out the transmission of a very weak electromagnetic resonator field. Nevertheless, to avoid sweeping the qubit frequency across the resonator frequency, one may choose larger detunings. We numerically integrate a master equation, alternating steps of Jaynes-Cummings interaction with single-qubit flip pulses. The Hamiltonian is easily diagonalized to yield the energy levels.

Quantum Criticality in the Biased Dicke Model

As a result of this transformation, the atoms become with frequencies equal to the difference between the energy levels. We now consider the critical behavior of the biased Dicke model which contains the term. We will discuss these arrangements further in the next sections. We will neglect the possible space dependence of g; this is discussed further in §3. Although the proposal in the paper involves a ring cavity and neutral atoms, the scheme would be well suited to an ion trap system with two cavity mode polarizations. The zero temperature phase transition of §5 b has not apparently been observed.

Quantum Criticality in the Biased Dicke Model

Therefore the excitation energy of the high-energy spectrum does not become zero even in the vicinity of the critical coupling. For N atoms to cooperatively interact with a single privileged mode of the radiation field, we require a special environment: one mode, or frequency, must dominate while other frequencies are suppressed. This approach can be labeled as analog-digital quantum simulation and corresponds to finding some terms in the simulated system that can be implemented in an analog way, e. Then the variances in the ground state can be calculate, which are given as where the subscripts denote the bosonic modes a and b respectively. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder in order to reproduce the material.

Study of Antigravity in an Model and in Brans

To obtain the best experience, we recommend you use a more up to date browser or turn off compatibility mode in Internet Explorer. Bose-Einstein condensation in a gas of sodium atoms. In addition, the timing of the atoms entering the cavity is uncertain and, as a result, if there are already N atoms in the cavity, and in the middle of an interaction with that cavity, then at the moment when one atom is gained or lost the change in cooperativity may not exactly match the change in atom number. The atoms are coupled with strength g shown as G N and decay at rate γ. In the presence of a cavity, the electromagnetic field is dominated by a single wavelength and direction and the Dicke model can potentially be realized. The biased Dicke model can be realized easily in the system of the flux qubits coupled to a quantum oscillator. The relatively large physical size compared with the atomic beam used for the atoms ensures that many atoms can easily be accommodated inside.

The Dicke model in quantum optics: Dicke model revisited

In these cases, the atoms of the Dicke model are replaced by superconducting qubits while the electromagnetic field remains. A transmon qubit of frequency ω q is interacting with a microwave resonator, whose transition frequency is ω r. The transition can be readily understood by the use of the applied to a. In , a superradiant phase transition is a that occurs in a collection of emitters such as atoms , between a state containing few electromagnetic excitations as in the and a with many electromagnetic excitations trapped inside the emitters. Reproduced with permission from Dimer et al. It has been shown in recent paper that the bias terms will create additional coupling to the environment and increase the fragility of non-classical states.

Digital Quantum Rabi and Dicke Models in Superconducting Circuits

When the coupling constant is below the critical value, the Eq. To minimize this loss, one can choose, for example, the transmon frequency in the second step to be tuned to the rotating frame, such that. The Dicke model was later introduced to generalize this interaction to an ensemble of N two-level systems. Fractal decomposition of exponential operators with applications to many-body theories and Monte Carlo simulations. Experimental evidence of this regime has been observed in the optical and microwave domains ,. One reason is that access is needed for laser cooling of the motional state of the ions.

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